Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. One starts at the root and explores as far as possible along each branch before backtracking.
A version of depth-first search was investigated in the 19th century by French mathematician Charles Pierre Trémaux as a strategy for solving mazes.

The order of Excution of nodes are as :1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Pseudo code:
Input: A graph G and a vertex v of G
Output: All vertices reachable from v labeled as discovered
A recursive implementation of DFS:
1 procedure DFS(G,v):
2 label v as discovered
3 for all edges from v to w in G.adjacentEdges(v) do
4 if vertex w is not labeled as discovered then
5 recursively call DFS(G,w)
A non-recursive implementation of DFS:
1 procedure DFS-iterative(G,v):
2 let S be a stack
3 S.push(v)
4 while S is not empty
5 v = S.pop()
6 if v is not labeled as discovered:
7 label v as discovered
8 for all edges from v to w in G.adjacentEdges(v) do
9 S.push(w)

Applications: There are various applications of DFS.
• Finding connected components.
• Detecting cycle in a graph.
• Finding connected components.
• Finding the bridges of a graph.
• Generating words in order to plot the Limit Set of a Group.
• Finding strongly connected components.
• Planarity testing.
• Solving puzzles with only one solution, such as mazes. (DFS can be adapted to find all solutions to a maze by only including nodes on the current path in the visited set.)
• Maze generation may use a randomized depth-first search.
• Finding biconnectivity in graphs.

Breadth-first search (BFS) is an algorithm for traversing or searching tree or graph data structures. It starts at the tree root (or some subjective node of a graph, sometimes referred to as a ‘search key’) and explores the neighbor nodes first, before moving to the next level neighbors.
BFS was invented in the late 1950s by E. F. Moore, who used it to find the shortest path out of a maze, and discovered independently by C. Y. Lee as a wire routing algorithm.

So traversal is: a, b, c, d, e, f, g, h, i , j, k.
Pseudocode:
Input: A graph Graph and a starting vertex root of G
Output: All vertices reachable from root labeled as explored.
A non-recursive implementation of breadth-first search:
1 Breadth-First-Search (Graph, root):
2
3 for each node n in Graph:
4 n.distance = INFINITY
5 n.parent = NIL
6
7 create empty queue Q
8
9 root.distance = 0
10 Q.enqueue(root)
11
12 while Q is not empty:
13
14 current = Q.dequeue()
15
16 for each node n that is adjacent to current:
17 if n.distance == INFINITY:
18 n.distance = current.distance + 1
19 n.parent = current
20 Q.enqueue(n)
Applications:
Breadth-first search can be used to solve many problems in graph theory, for example:
• Shortest Path and Minimum Spanning Tree for unweighted graph.
• Peer to Peer Networks.
• Social Networking Websites.
• In Garbage Collection.
• Path Finding.
• Finding all nodes within one connected component.